Understanding the stability of the G matrix in natural populations is fundamental for predicting evolutionary trajectories, yet, the extent of its spatial variation and how this impacts responses to selection remain open questions. With a nested paternal half-sib crossing design and plants grown in a field experiment, we examined differences in the genetic architecture of flowering time, floral display and plant size among four Scandinavian populations of Arabidopsis lyrata. Using a multivariate Bayesian framework, we compared the size, shape and orientation of G matrices and assessed their potential to facilitate or constrain trait evolution. Flowering time, floral display and rosette size varied among populations and significant additive genetic variation within populations indicated potential to evolve in response to selection. Yet, some characters, including flowering start and number of flowers, may not evolve independently because of genetic correlations. Using a multivariate framework, we found few differences in the genetic architecture of traits among populations. G matrices varied mostly in size rather than shape or orientation. Differences in multivariate responses to selection predicted from differences in G were small, suggesting overall matrix similarity and shared constraints to trait evolution among populations.